IB Physics HL D.1.2 Universal Gravitation Question Bank

Practise IB Physics HL D.1.2 by solving universal-gravitation force, mass, orbit and large-scale astrophysics problems.

[Maximum number: 3]

There is a proposal to place a satellite in orbit around planet Mars.

The satellite is to have an orbital time T equal to the length of a day on Mars. It can be shown that

T^{2}=k R^{3}

where R is the orbital radius of the satellite and k is a constant.

Mars has a mass of $6.4 \times 10^{23} \mathrm{~kg}$ . Show that, for Mars, k is about $9 \times 10^{-13} \mathrm{~s}^{2} \mathrm{~m}^{-3}$ .

« $\frac{m v^{2}}{r}=\frac{G M m}{r^{2}}$ hence» $v=\sqrt{\frac{G M}{R}}$ . Also $v=\frac{2 \pi R}{T}$

OR
$m \omega^{2} r=\frac{G M m}{r^{2}} \text { hence } \omega^{2}=\frac{G M}{R^{3}}$

uses either of the above to get $T^{2}=\frac{4 \pi^{2}}{G M} R^{3}$

OR uses $k=\frac{4 \pi^{2}}{G M}$ $k=9.2 \times 10^{-13} / 9.3 \times 10^{-13}$

Unit not required

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D.1.2—Universal gravitation question 1